Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample32.0ms

Algorithm

intervals

Results

8.0ms	55×	body	640	valid
7.0ms	38×	body	1280	valid
5.0ms	134×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	9	11

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 116

Calls

3 calls:

5.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
29.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
14.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4975	1654
1	4975	1654

prune218.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	11	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 18.0b

Counts

126 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
2.2b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 76

Calls

3 calls:

16.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series44.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
9.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5302	1342

prune151.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	89	7	96

Merged error: 0.3b

Counts

96 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative`

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
19.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
34.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4962	2089
1	4962	2089

prune257.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Merged error: 0.0b

Counts

144 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0)))))
0.1b	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0))))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
67×	`times-frac`
55×	`*-un-lft-identity`
53×	`add-cube-cbrt`
34×	`sqrt-prod`
29×	`associate-r`
28×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`flip3-+` `associate-*r/` `flip-+`
10×	`pow1` `sqrt-div` `associate-/r*` `unswap-sqr`
8×	`frac-add`
7×	`distribute-rgt-out`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-unprod` `associate-*l/` `distribute-lft-out`

Counts

4 → 179

Calls

4 calls:

7.0ms	(/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0)))))
19.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0))))))
10.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0)))))
17.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ x 1.0) (* (sqrt x) (sqrt (+ x 1.0))))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))

simplify62.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5492	3143

prune333.0ms

Filtered

149 candidates to 191 candidates (-28.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	192	11	203

Merged error: 0.0b

Counts

203 → 11

regimes59.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	14	18

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample838.0ms

Algorithm

intervals

Results

280.0ms	1896×	body	640	valid
220.0ms	1151×	body	1280	valid
156.0ms	4002×	body	80	valid
69.0ms	642×	body	320	valid
22.0ms	309×	body	160	valid

Details

analyze1.0ms

sample32.0ms

simplify3.0ms

prune5.0ms

localize7.0ms

rewrite43.0ms

series28.0ms

simplify47.0ms

prune218.0ms

localize9.0ms

rewrite36.0ms

series44.0ms

simplify36.0ms

prune151.0ms

localize13.0ms

rewrite50.0ms

series55.0ms

simplify46.0ms

prune257.0ms

localize10.0ms

rewrite47.0ms

series41.0ms

simplify62.0ms

prune333.0ms

regimes59.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample838.0ms

Profiling